%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : GRP125-3.005 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 12:38:01 PM UTC 2026
% Result : Unsatisfiable 7.26s 1.69s
% Output : CNFRefutation 7.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 37
% Syntax : Number of clauses : 332 ( 109 unt; 150 nHn; 330 RR)
% Number of literals : 869 ( 0 equ; 274 neg)
% Maximal clause size : 7 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 6 con; 0-0 aty)
% Number of variables : 166 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(e_2_is_not_e_1,axiom,
~ equalish(e_2,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_1) ).
cnf(product_left_cancellation,axiom,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_left_cancellation) ).
cnf(e_5_is_not_e_3,axiom,
~ equalish(e_5,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_is_not_e_3) ).
cnf(cycle7,axiom,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle7) ).
cnf(cycle2,axiom,
( ~ group_element(X1)
| cycle(X1,e_4)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle2) ).
cnf(product_total_function1,axiom,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function1) ).
cnf(e_4_is_not_e_3,axiom,
~ equalish(e_4,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_3) ).
cnf(e_2_is_not_e_3,axiom,
~ equalish(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_3) ).
cnf(e_3_is_not_e_1,axiom,
~ equalish(e_3,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_1) ).
cnf(element_2,axiom,
group_element(e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_2) ).
cnf(element_1,axiom,
group_element(e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_1) ).
cnf(product_idempotence,axiom,
product(X1,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_idempotence) ).
cnf(e_5_is_not_e_4,axiom,
~ equalish(e_5,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_is_not_e_4) ).
cnf(e_3_is_not_e_4,axiom,
~ equalish(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_4) ).
cnf(e_2_is_not_e_4,axiom,
~ equalish(e_2,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_4) ).
cnf(e_1_greater_e_0,axiom,
greater(e_1,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_greater_e_0) ).
cnf(e_2_then_e_3,axiom,
next(e_2,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_then_e_3) ).
cnf(element_3,axiom,
group_element(e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_3) ).
cnf(cycle6,axiom,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cycle6) ).
cnf(e_3_then_e_4,axiom,
next(e_3,e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_then_e_4) ).
cnf(e_4_is_not_e_1,axiom,
~ equalish(e_4,e_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_1) ).
cnf(product_right_cancellation,axiom,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_right_cancellation) ).
cnf(e_1_is_not_e_5,axiom,
~ equalish(e_1,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_1_is_not_e_5) ).
cnf(e_5_greater_e_2,axiom,
greater(e_5,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_2) ).
cnf(e_4_greater_e_0,axiom,
greater(e_4,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_0) ).
cnf(element_4,axiom,
group_element(e_4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_4) ).
cnf(e_4_is_not_e_5,axiom,
~ equalish(e_4,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_is_not_e_5) ).
cnf(product_total_function2,axiom,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_total_function2) ).
cnf(e_5_greater_e_3,axiom,
greater(e_5,e_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_5_greater_e_3) ).
cnf(e_3_greater_e_0,axiom,
greater(e_3,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_greater_e_0) ).
cnf(qg3,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qg3) ).
cnf(e_3_is_not_e_5,axiom,
~ equalish(e_3,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_5) ).
cnf(element_5,axiom,
group_element(e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',element_5) ).
cnf(e_2_greater_e_0,axiom,
greater(e_2,e_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_greater_e_0) ).
cnf(e_4_greater_e_2,axiom,
greater(e_4,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_4_greater_e_2) ).
cnf(e_2_is_not_e_5,axiom,
~ equalish(e_2,e_5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_2_is_not_e_5) ).
cnf(e_3_is_not_e_2,axiom,
~ equalish(e_3,e_2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e_3_is_not_e_2) ).
cnf(c_0_37,plain,
~ equalish(e_2,e_1),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_1]) ).
cnf(c_0_38,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
inference(fof_simplification,[status(thm)],[product_left_cancellation]) ).
cnf(c_0_39,plain,
~ equalish(e_5,e_3),
inference(fof_simplification,[status(thm)],[e_5_is_not_e_3]) ).
cnf(c_0_40,plain,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[cycle7]) ).
cnf(c_0_41,plain,
( ~ group_element(X1)
| cycle(X1,e_4)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
inference(fof_simplification,[status(thm)],[cycle2]) ).
cnf(c_0_42,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
inference(fof_simplification,[status(thm)],[product_total_function1]) ).
cnf(c_0_43,plain,
~ equalish(e_2,e_1),
c_0_37 ).
cnf(c_0_44,plain,
( ~ product(X4,X2,X3)
| ~ product(X1,X2,X3)
| equalish(X1,X4) ),
c_0_38 ).
cnf(c_0_45,plain,
~ equalish(e_4,e_3),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_3]) ).
cnf(c_0_46,plain,
~ equalish(e_2,e_3),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_3]) ).
cnf(c_0_47,plain,
~ equalish(e_3,e_1),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_1]) ).
cnf(c_0_48,plain,
~ equalish(e_5,e_3),
c_0_39 ).
cnf(c_0_49,plain,
( ~ next(X1,X4)
| ~ greater(X2,e_0)
| ~ product(X1,e_1,X3)
| ~ cycle(X1,X2)
| equalish(X3,X4) ),
c_0_40 ).
cnf(c_0_50,plain,
( ~ group_element(X1)
| cycle(X1,e_4)
| cycle(X1,e_3)
| cycle(X1,e_2)
| cycle(X1,e_1)
| cycle(X1,e_0) ),
c_0_41 ).
cnf(c_0_51,axiom,
group_element(e_2),
element_2 ).
cnf(c_0_52,plain,
( ~ group_element(X2)
| ~ group_element(X1)
| product(X1,X2,e_5)
| product(X1,X2,e_4)
| product(X1,X2,e_3)
| product(X1,X2,e_2)
| product(X1,X2,e_1) ),
c_0_42 ).
cnf(c_0_53,axiom,
group_element(e_1),
element_1 ).
cnf(c_0_54,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_55,axiom,
product(X1,X1,X1),
product_idempotence ).
cnf(c_0_56,plain,
~ equalish(e_4,e_3),
c_0_45 ).
cnf(c_0_57,plain,
~ equalish(e_2,e_3),
c_0_46 ).
cnf(c_0_58,plain,
~ equalish(e_5,e_4),
inference(fof_simplification,[status(thm)],[e_5_is_not_e_4]) ).
cnf(c_0_59,plain,
~ equalish(e_3,e_1),
c_0_47 ).
cnf(c_0_60,plain,
~ equalish(e_3,e_4),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_4]) ).
cnf(c_0_61,plain,
~ equalish(e_2,e_4),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_4]) ).
cnf(c_0_62,plain,
( ~ next(X1,e_3)
| ~ greater(X2,e_0)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_63,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_1)
| cycle(e_2,e_2)
| cycle(e_2,e_3)
| cycle(e_2,e_4) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_64,axiom,
greater(e_1,e_0),
e_1_greater_e_0 ).
cnf(c_0_65,axiom,
next(e_2,e_3),
e_2_then_e_3 ).
cnf(c_0_66,plain,
( ~ group_element(X1)
| product(X1,e_1,e_1)
| product(X1,e_1,e_2)
| product(X1,e_1,e_3)
| product(X1,e_1,e_4)
| product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_67,plain,
~ product(e_2,e_1,e_1),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_68,plain,
( ~ next(X1,e_3)
| ~ greater(X2,e_0)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_56,c_0_49]) ).
cnf(c_0_69,plain,
( ~ next(X1,e_3)
| ~ greater(X2,e_0)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_57,c_0_49]) ).
cnf(c_0_70,plain,
~ equalish(e_5,e_4),
c_0_58 ).
cnf(c_0_71,axiom,
group_element(e_3),
element_3 ).
cnf(c_0_72,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_44]) ).
cnf(c_0_73,plain,
~ equalish(e_3,e_4),
c_0_60 ).
cnf(c_0_74,plain,
~ equalish(e_2,e_4),
c_0_61 ).
cnf(c_0_75,plain,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
inference(fof_simplification,[status(thm)],[cycle6]) ).
cnf(c_0_76,plain,
( ~ product(e_2,e_1,e_5)
| cycle(e_2,e_4)
| cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_77,plain,
( product(e_2,e_1,e_5)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_51]),c_0_67]) ).
cnf(c_0_78,plain,
( ~ product(e_2,e_1,e_4)
| cycle(e_2,e_4)
| cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_79,plain,
( ~ product(e_2,e_1,e_2)
| cycle(e_2,e_4)
| cycle(e_2,e_3)
| cycle(e_2,e_2)
| cycle(e_2,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_63]),c_0_64]),c_0_65])]) ).
cnf(c_0_80,plain,
( ~ next(X1,e_4)
| ~ greater(X2,e_0)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_70,c_0_49]) ).
cnf(c_0_81,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_1)
| cycle(e_3,e_2)
| cycle(e_3,e_3)
| cycle(e_3,e_4) ),
inference(spm,[status(thm)],[c_0_50,c_0_71]) ).
cnf(c_0_82,axiom,
next(e_3,e_4),
e_3_then_e_4 ).
cnf(c_0_83,plain,
~ product(e_3,e_1,e_1),
inference(spm,[status(thm)],[c_0_72,c_0_55]) ).
cnf(c_0_84,plain,
( ~ next(X1,e_4)
| ~ greater(X2,e_0)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_73,c_0_49]) ).
cnf(c_0_85,plain,
( ~ next(X1,e_4)
| ~ greater(X2,e_0)
| ~ cycle(X1,X2)
| ~ product(X1,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_74,c_0_49]) ).
cnf(c_0_86,plain,
( ~ greater(X2,X1)
| ~ product(X1,e_1,X2)
| ~ cycle(X1,e_0) ),
c_0_75 ).
cnf(c_0_87,plain,
( cycle(e_2,e_0)
| cycle(e_2,e_2)
| cycle(e_2,e_3)
| cycle(e_2,e_4)
| product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_77]),c_0_78]),c_0_79]) ).
cnf(c_0_88,plain,
~ equalish(e_4,e_1),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_1]) ).
cnf(c_0_89,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
inference(fof_simplification,[status(thm)],[product_right_cancellation]) ).
cnf(c_0_90,plain,
~ equalish(e_1,e_5),
inference(fof_simplification,[status(thm)],[e_1_is_not_e_5]) ).
cnf(c_0_91,plain,
( ~ product(e_3,e_1,e_5)
| cycle(e_3,e_4)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_64]),c_0_82])]) ).
cnf(c_0_92,plain,
( product(e_3,e_1,e_5)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_71]),c_0_83]) ).
cnf(c_0_93,plain,
( ~ product(e_3,e_1,e_3)
| cycle(e_3,e_4)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_81]),c_0_64]),c_0_82])]) ).
cnf(c_0_94,plain,
( ~ product(e_3,e_1,e_2)
| cycle(e_3,e_4)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| cycle(e_3,e_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_81]),c_0_64]),c_0_82])]) ).
cnf(c_0_95,plain,
( ~ greater(X1,e_2)
| ~ product(e_2,e_1,X1)
| cycle(e_2,e_4)
| cycle(e_2,e_3)
| cycle(e_2,e_2)
| product(e_2,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_96,axiom,
greater(e_5,e_2),
e_5_greater_e_2 ).
cnf(c_0_97,plain,
~ equalish(e_4,e_1),
c_0_88 ).
cnf(c_0_98,plain,
( ~ product(X1,X4,X3)
| ~ product(X1,X2,X3)
| equalish(X2,X4) ),
c_0_89 ).
cnf(c_0_99,plain,
~ equalish(e_1,e_5),
c_0_90 ).
cnf(c_0_100,plain,
( cycle(e_3,e_0)
| cycle(e_3,e_2)
| cycle(e_3,e_3)
| cycle(e_3,e_4)
| product(e_3,e_1,e_4) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_93]),c_0_94]) ).
cnf(c_0_101,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_3)
| cycle(e_2,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_77]),c_0_96])]) ).
cnf(c_0_102,axiom,
greater(e_4,e_0),
e_4_greater_e_0 ).
cnf(c_0_103,axiom,
group_element(e_4),
element_4 ).
cnf(c_0_104,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_105,plain,
~ equalish(e_4,e_5),
inference(fof_simplification,[status(thm)],[e_4_is_not_e_5]) ).
cnf(c_0_106,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
inference(fof_simplification,[status(thm)],[product_total_function2]) ).
cnf(c_0_107,plain,
( ~ product(e_1,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_99,c_0_44]) ).
cnf(c_0_108,plain,
( ~ greater(X1,e_3)
| ~ product(e_3,e_1,X1)
| cycle(e_3,e_4)
| cycle(e_3,e_3)
| cycle(e_3,e_2)
| product(e_3,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_86,c_0_100]) ).
cnf(c_0_109,axiom,
greater(e_5,e_3),
e_5_greater_e_3 ).
cnf(c_0_110,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_2)
| product(e_2,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_101]),c_0_102]),c_0_65])]),c_0_77]) ).
cnf(c_0_111,axiom,
greater(e_3,e_0),
e_3_greater_e_0 ).
cnf(c_0_112,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
inference(fof_simplification,[status(thm)],[qg3]) ).
cnf(c_0_113,plain,
( ~ group_element(X1)
| product(X1,e_4,e_1)
| product(X1,e_4,e_2)
| product(X1,e_4,e_3)
| product(X1,e_4,e_4)
| product(X1,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_52,c_0_103]) ).
cnf(c_0_114,plain,
~ product(e_1,e_4,e_1),
inference(spm,[status(thm)],[c_0_104,c_0_55]) ).
cnf(c_0_115,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_1,X1,X2) ),
inference(spm,[status(thm)],[c_0_97,c_0_44]) ).
cnf(c_0_116,plain,
~ equalish(e_4,e_5),
c_0_105 ).
cnf(c_0_117,plain,
( ~ product(X1,X2,X4)
| ~ product(X1,X2,X3)
| equalish(X3,X4) ),
c_0_106 ).
cnf(c_0_118,plain,
~ equalish(e_3,e_5),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_5]) ).
cnf(c_0_119,axiom,
group_element(e_5),
element_5 ).
cnf(c_0_120,plain,
~ product(e_5,e_1,e_1),
inference(spm,[status(thm)],[c_0_107,c_0_55]) ).
cnf(c_0_121,plain,
( cycle(e_3,e_2)
| cycle(e_3,e_3)
| cycle(e_3,e_4)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_92]),c_0_109])]) ).
cnf(c_0_122,plain,
( cycle(e_2,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_110]),c_0_111]),c_0_65])]),c_0_77]) ).
cnf(c_0_123,axiom,
greater(e_2,e_0),
e_2_greater_e_0 ).
cnf(c_0_124,negated_conjecture,
( ~ product(X2,X1,X4)
| ~ product(X1,X2,X3)
| product(X3,X4,X1) ),
c_0_112 ).
cnf(c_0_125,plain,
( product(e_1,e_4,e_5)
| product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_53]),c_0_114]) ).
cnf(c_0_126,plain,
~ product(e_4,e_1,e_1),
inference(spm,[status(thm)],[c_0_115,c_0_55]) ).
cnf(c_0_127,plain,
( ~ product(X1,X2,e_4)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_116,c_0_117]) ).
cnf(c_0_128,plain,
~ equalish(e_3,e_5),
c_0_118 ).
cnf(c_0_129,plain,
( ~ product(X1,e_1,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_99,c_0_98]) ).
cnf(c_0_130,plain,
( product(e_5,e_1,e_5)
| product(e_5,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_119]),c_0_120]) ).
cnf(c_0_131,plain,
( cycle(e_3,e_3)
| cycle(e_3,e_2)
| product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_121]),c_0_102]),c_0_82])]),c_0_92]) ).
cnf(c_0_132,plain,
( product(e_2,e_1,e_4)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_122]),c_0_123]),c_0_65])]),c_0_77]) ).
cnf(c_0_133,axiom,
greater(e_4,e_2),
e_4_greater_e_2 ).
cnf(c_0_134,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_5,e_4)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]) ).
cnf(c_0_135,plain,
( product(e_4,e_1,e_5)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_103]),c_0_126]) ).
cnf(c_0_136,plain,
~ product(e_5,e_5,e_4),
inference(spm,[status(thm)],[c_0_127,c_0_55]) ).
cnf(c_0_137,plain,
~ equalish(e_2,e_5),
inference(fof_simplification,[status(thm)],[e_2_is_not_e_5]) ).
cnf(c_0_138,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_128,c_0_44]) ).
cnf(c_0_139,plain,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_129,c_0_130]),c_0_55])]) ).
cnf(c_0_140,plain,
( cycle(e_3,e_2)
| product(e_3,e_1,e_4)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_131]),c_0_111]),c_0_82])]),c_0_92]) ).
cnf(c_0_141,plain,
~ equalish(e_3,e_2),
inference(fof_simplification,[status(thm)],[e_3_is_not_e_2]) ).
cnf(c_0_142,plain,
( cycle(e_2,e_2)
| cycle(e_2,e_3)
| cycle(e_2,e_4)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_132]),c_0_133])]) ).
cnf(c_0_143,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_135]),c_0_136]) ).
cnf(c_0_144,plain,
~ equalish(e_2,e_5),
c_0_137 ).
cnf(c_0_145,plain,
( ~ product(e_3,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_138,c_0_139]) ).
cnf(c_0_146,plain,
( product(e_3,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_4) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_140]),c_0_123]),c_0_82])]),c_0_92]) ).
cnf(c_0_147,plain,
~ equalish(e_3,e_2),
c_0_141 ).
cnf(c_0_148,plain,
( cycle(e_2,e_3)
| cycle(e_2,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_142]),c_0_102]),c_0_65])]),c_0_132]) ).
cnf(c_0_149,negated_conjecture,
( ~ product(e_1,e_4,X1)
| product(X1,e_5,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_135]) ).
cnf(c_0_150,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_143]),c_0_55])]) ).
cnf(c_0_151,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_44]) ).
cnf(c_0_152,plain,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_153,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_2,X1,X2) ),
inference(spm,[status(thm)],[c_0_147,c_0_44]) ).
cnf(c_0_154,plain,
( cycle(e_2,e_2)
| product(e_2,e_1,e_3)
| product(e_2,e_1,e_2) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_148]),c_0_111]),c_0_65])]),c_0_132]) ).
cnf(c_0_155,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_3,e_5,e_1)
| product(e_1,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_149,c_0_150]) ).
cnf(c_0_156,plain,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_152]),c_0_153]) ).
cnf(c_0_157,plain,
( product(e_2,e_1,e_2)
| product(e_2,e_1,e_3) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_154]),c_0_123]),c_0_65])]),c_0_132]) ).
cnf(c_0_158,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_149,c_0_155]) ).
cnf(c_0_159,plain,
( ~ product(e_4,X1,X2)
| ~ product(e_5,X1,X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_44]) ).
cnf(c_0_160,plain,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_156,c_0_157]) ).
cnf(c_0_161,plain,
( ~ product(e_3,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_44]) ).
cnf(c_0_162,plain,
( ~ product(e_2,X1,X2)
| ~ product(e_4,X1,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_44]) ).
cnf(c_0_163,negated_conjecture,
( product(e_3,e_5,e_1)
| product(e_2,e_5,e_1)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_158]),c_0_55])]) ).
cnf(c_0_164,plain,
~ product(e_4,e_1,e_2),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_160]),c_0_161]),c_0_162]) ).
cnf(c_0_165,plain,
( ~ product(e_4,e_1,e_3)
| product(e_3,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_152]),c_0_161]) ).
cnf(c_0_166,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_128,c_0_98]) ).
cnf(c_0_167,negated_conjecture,
( product(e_4,e_1,e_3)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(sr,[status(thm)],[c_0_163,c_0_164]) ).
cnf(c_0_168,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_3,e_1,e_2)
| product(e_4,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_165,c_0_163]) ).
cnf(c_0_169,plain,
( ~ group_element(X1)
| product(X1,e_3,e_1)
| product(X1,e_3,e_2)
| product(X1,e_3,e_3)
| product(X1,e_3,e_4)
| product(X1,e_3,e_5) ),
inference(spm,[status(thm)],[c_0_52,c_0_71]) ).
cnf(c_0_170,plain,
~ product(e_5,e_3,e_5),
inference(spm,[status(thm)],[c_0_166,c_0_55]) ).
cnf(c_0_171,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_3,e_5,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_162,c_0_167]) ).
cnf(c_0_172,negated_conjecture,
( ~ product(e_2,e_1,e_2)
| product(e_3,e_5,e_1)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_168]),c_0_153]),c_0_162]) ).
cnf(c_0_173,plain,
( product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2)
| product(e_5,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_119]),c_0_170]) ).
cnf(c_0_174,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_59,c_0_117]) ).
cnf(c_0_175,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_171,c_0_157]),c_0_172]) ).
cnf(c_0_176,negated_conjecture,
( ~ product(e_3,e_5,X1)
| product(X1,e_1,e_3)
| product(e_5,e_3,e_2)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_173]) ).
cnf(c_0_177,plain,
~ product(e_1,e_1,e_3),
inference(spm,[status(thm)],[c_0_174,c_0_55]) ).
cnf(c_0_178,negated_conjecture,
( ~ product(e_5,e_3,X1)
| product(X1,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_124,c_0_175]) ).
cnf(c_0_179,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_5,e_3,e_3)
| product(e_5,e_3,e_2)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_176,c_0_175]),c_0_177]) ).
cnf(c_0_180,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_4,e_1,e_5)
| product(e_5,e_3,e_2)
| product(e_5,e_3,e_3) ),
inference(spm,[status(thm)],[c_0_178,c_0_179]) ).
cnf(c_0_181,negated_conjecture,
( product(e_5,e_3,e_2)
| product(e_4,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_180]),c_0_55])]) ).
cnf(c_0_182,negated_conjecture,
( ~ product(e_3,e_5,X1)
| product(X1,e_2,e_3)
| product(e_2,e_5,e_1)
| product(e_4,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_124,c_0_181]) ).
cnf(c_0_183,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_2,e_5,e_1)
| product(e_1,e_2,e_3) ),
inference(spm,[status(thm)],[c_0_182,c_0_175]) ).
cnf(c_0_184,plain,
( ~ product(X1,X2,e_3)
| ~ product(X1,X2,e_2) ),
inference(spm,[status(thm)],[c_0_147,c_0_117]) ).
cnf(c_0_185,negated_conjecture,
( ~ product(e_2,e_1,X1)
| product(X1,e_3,e_2)
| product(e_2,e_5,e_1)
| product(e_4,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_124,c_0_183]) ).
cnf(c_0_186,plain,
~ product(e_3,e_3,e_2),
inference(spm,[status(thm)],[c_0_184,c_0_55]) ).
cnf(c_0_187,negated_conjecture,
( product(e_4,e_1,e_5)
| product(e_2,e_5,e_1)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_185,c_0_157]),c_0_186]) ).
cnf(c_0_188,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_5) ),
inference(spm,[status(thm)],[c_0_144,c_0_117]) ).
cnf(c_0_189,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_1,e_5)
| product(e_4,e_1,e_5) ),
inference(spm,[status(thm)],[c_0_178,c_0_181]) ).
cnf(c_0_190,negated_conjecture,
( ~ product(e_2,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_162,c_0_187]),c_0_188]) ).
cnf(c_0_191,negated_conjecture,
( product(e_1,e_4,e_4)
| product(e_1,e_4,e_3)
| product(e_1,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_134,c_0_189]),c_0_136]),c_0_190]) ).
cnf(c_0_192,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_150]) ).
cnf(c_0_193,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_2)
| product(e_1,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_191]),c_0_55])]) ).
cnf(c_0_194,plain,
( ~ product(X1,e_4,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_116,c_0_98]) ).
cnf(c_0_195,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_1,e_4,e_2)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_192,c_0_135]) ).
cnf(c_0_196,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_124,c_0_193]) ).
cnf(c_0_197,plain,
~ product(e_5,e_4,e_5),
inference(spm,[status(thm)],[c_0_194,c_0_55]) ).
cnf(c_0_198,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_59,c_0_98]) ).
cnf(c_0_199,negated_conjecture,
( product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_149,c_0_195]) ).
cnf(c_0_200,negated_conjecture,
( ~ product(e_1,e_4,X1)
| product(X1,e_5,e_1)
| product(e_2,e_1,e_5)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_124,c_0_189]) ).
cnf(c_0_201,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_2)
| product(e_5,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_196,c_0_189]),c_0_190]) ).
cnf(c_0_202,plain,
( product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_119]),c_0_197]) ).
cnf(c_0_203,plain,
~ product(e_2,e_4,e_4),
inference(spm,[status(thm)],[c_0_162,c_0_55]) ).
cnf(c_0_204,plain,
( ~ product(e_5,e_3,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_198,c_0_139]) ).
cnf(c_0_205,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_2,e_5,e_1)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_199,c_0_164]) ).
cnf(c_0_206,plain,
( ~ product(e_4,e_1,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_159,c_0_139]) ).
cnf(c_0_207,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_5,e_3,e_4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_200,c_0_201]),c_0_190]) ).
cnf(c_0_208,plain,
( ~ product(e_2,e_4,e_1)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_4) ),
inference(spm,[status(thm)],[c_0_151,c_0_202]) ).
cnf(c_0_209,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_51]),c_0_203]) ).
cnf(c_0_210,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_4,e_1,e_3)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_205]),c_0_206]) ).
cnf(c_0_211,negated_conjecture,
( ~ product(e_3,e_5,X1)
| product(X1,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_124,c_0_207]) ).
cnf(c_0_212,plain,
( product(e_5,e_4,e_4)
| product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_208,c_0_209]) ).
cnf(c_0_213,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_1,X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_98]) ).
cnf(c_0_214,plain,
( ~ product(e_2,e_4,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_104,c_0_157]) ).
cnf(c_0_215,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_2,e_5,e_1)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_210]),c_0_162]) ).
cnf(c_0_216,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_1,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_211,c_0_175]) ).
cnf(c_0_217,plain,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_3)
| product(e_2,e_4,e_2)
| product(e_5,e_4,e_2)
| product(e_5,e_4,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_159,c_0_212]),c_0_55])]) ).
cnf(c_0_218,plain,
~ product(e_2,e_4,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_214]),c_0_55])]) ).
cnf(c_0_219,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_1,e_4,e_2)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4) ),
inference(sr,[status(thm)],[c_0_195,c_0_164]) ).
cnf(c_0_220,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_2,e_5,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_215,c_0_157]) ).
cnf(c_0_221,negated_conjecture,
( ~ product(e_5,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_107,c_0_216]) ).
cnf(c_0_222,plain,
( product(e_5,e_4,e_3)
| product(e_5,e_4,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_217,c_0_218]) ).
cnf(c_0_223,negated_conjecture,
( ~ product(e_4,e_1,X1)
| product(X1,e_2,e_4)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_3)
| product(e_5,e_3,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_219]) ).
cnf(c_0_224,plain,
( product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_4,e_1,e_5) ),
inference(sr,[status(thm)],[c_0_135,c_0_164]) ).
cnf(c_0_225,negated_conjecture,
( ~ product(e_5,e_4,e_2)
| product(e_2,e_1,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_104,c_0_220]) ).
cnf(c_0_226,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_5,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_221,c_0_222]) ).
cnf(c_0_227,negated_conjecture,
( product(e_5,e_3,e_4)
| product(e_4,e_1,e_3)
| product(e_4,e_1,e_4)
| product(e_5,e_2,e_4) ),
inference(spm,[status(thm)],[c_0_223,c_0_224]) ).
cnf(c_0_228,plain,
( ~ product(e_5,e_2,e_4)
| product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_213,c_0_139]) ).
cnf(c_0_229,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_2,e_1,e_2)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_225,c_0_226]) ).
cnf(c_0_230,negated_conjecture,
( product(e_5,e_1,e_2)
| product(e_5,e_1,e_3)
| product(e_4,e_1,e_3) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_204,c_0_227]),c_0_206]),c_0_228]) ).
cnf(c_0_231,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_2,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_229]),c_0_55])]) ).
cnf(c_0_232,plain,
( product(e_2,e_4,e_1)
| product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(sr,[status(thm)],[c_0_209,c_0_218]) ).
cnf(c_0_233,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_151,c_0_230]),c_0_162]) ).
cnf(c_0_234,plain,
( ~ group_element(X1)
| product(X1,e_5,e_1)
| product(X1,e_5,e_2)
| product(X1,e_5,e_3)
| product(X1,e_5,e_4)
| product(X1,e_5,e_5) ),
inference(spm,[status(thm)],[c_0_52,c_0_119]) ).
cnf(c_0_235,plain,
~ product(e_1,e_5,e_1),
inference(spm,[status(thm)],[c_0_129,c_0_55]) ).
cnf(c_0_236,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_98]) ).
cnf(c_0_237,negated_conjecture,
( product(e_2,e_4,e_2)
| product(e_2,e_4,e_5) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_194,c_0_231]),c_0_232]) ).
cnf(c_0_238,negated_conjecture,
( ~ product(e_1,e_5,X1)
| ~ product(e_2,e_1,e_3)
| product(X1,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_124,c_0_233]) ).
cnf(c_0_239,plain,
( product(e_1,e_5,e_5)
| product(e_1,e_5,e_4)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_53]),c_0_235]) ).
cnf(c_0_240,plain,
~ product(e_2,e_3,e_3),
inference(spm,[status(thm)],[c_0_153,c_0_55]) ).
cnf(c_0_241,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_4,X2) ),
inference(spm,[status(thm)],[c_0_74,c_0_98]) ).
cnf(c_0_242,negated_conjecture,
( ~ product(e_2,e_3,e_5)
| product(e_2,e_4,e_2) ),
inference(spm,[status(thm)],[c_0_236,c_0_237]) ).
cnf(c_0_243,negated_conjecture,
( ~ product(e_1,e_5,X1)
| product(X1,e_2,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_238,c_0_157]) ).
cnf(c_0_244,plain,
( product(e_1,e_5,e_2)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_4) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_239]),c_0_55])]) ).
cnf(c_0_245,plain,
( product(e_2,e_3,e_5)
| product(e_2,e_3,e_4)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_169,c_0_51]),c_0_240]) ).
cnf(c_0_246,negated_conjecture,
~ product(e_2,e_3,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_241,c_0_242]),c_0_55])]) ).
cnf(c_0_247,plain,
( ~ product(X1,e_2,X2)
| ~ product(X1,e_5,X2) ),
inference(spm,[status(thm)],[c_0_144,c_0_98]) ).
cnf(c_0_248,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_151,c_0_207]) ).
cnf(c_0_249,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_243,c_0_244]) ).
cnf(c_0_250,plain,
( ~ product(X1,e_3,X2)
| ~ product(X1,e_2,X2) ),
inference(spm,[status(thm)],[c_0_147,c_0_98]) ).
cnf(c_0_251,plain,
( product(e_2,e_3,e_1)
| product(e_2,e_3,e_2)
| product(e_2,e_3,e_4) ),
inference(sr,[status(thm)],[c_0_245,c_0_246]) ).
cnf(c_0_252,negated_conjecture,
( ~ product(e_2,e_3,e_4)
| ~ product(e_2,e_2,e_1) ),
inference(spm,[status(thm)],[c_0_247,c_0_248]) ).
cnf(c_0_253,negated_conjecture,
( ~ product(e_5,e_1,X1)
| product(X1,e_4,e_5)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_124,c_0_244]) ).
cnf(c_0_254,negated_conjecture,
( ~ product(e_5,e_1,X1)
| product(X1,e_3,e_5)
| product(e_1,e_5,e_2)
| product(e_4,e_2,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_124,c_0_249]) ).
cnf(c_0_255,plain,
( ~ product(e_2,e_2,e_1)
| product(e_2,e_3,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_251]),c_0_252]) ).
cnf(c_0_256,negated_conjecture,
( ~ product(e_2,e_1,e_3)
| product(e_1,e_5,e_2)
| product(e_1,e_5,e_3)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_253,c_0_233]) ).
cnf(c_0_257,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_2,e_1)
| product(e_1,e_5,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_254,c_0_233]),c_0_246]),c_0_157]) ).
cnf(c_0_258,plain,
~ product(e_2,e_2,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_255]),c_0_55])]) ).
cnf(c_0_259,negated_conjecture,
( product(e_2,e_4,e_5)
| product(e_1,e_5,e_3)
| product(e_1,e_5,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_256,c_0_157]) ).
cnf(c_0_260,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_4,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_257]),c_0_258]) ).
cnf(c_0_261,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_2,e_1)
| product(e_1,e_5,e_2)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_243,c_0_259]) ).
cnf(c_0_262,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_161,c_0_260]) ).
cnf(c_0_263,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_5)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_243,c_0_261]),c_0_258]) ).
cnf(c_0_264,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_2,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_262,c_0_263]) ).
cnf(c_0_265,negated_conjecture,
product(e_2,e_4,e_5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_264]),c_0_55])]) ).
cnf(c_0_266,negated_conjecture,
( ~ product(e_4,e_2,X1)
| product(X1,e_5,e_4) ),
inference(spm,[status(thm)],[c_0_124,c_0_265]) ).
cnf(c_0_267,plain,
~ product(e_2,e_5,e_5),
inference(spm,[status(thm)],[c_0_151,c_0_55]) ).
cnf(c_0_268,plain,
( ~ product(e_2,e_5,e_3)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_129,c_0_157]) ).
cnf(c_0_269,negated_conjecture,
( product(e_1,e_5,e_4)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_266,c_0_260]) ).
cnf(c_0_270,plain,
~ product(e_3,e_4,e_4),
inference(spm,[status(thm)],[c_0_161,c_0_55]) ).
cnf(c_0_271,plain,
( product(e_2,e_5,e_4)
| product(e_2,e_5,e_3)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_51]),c_0_267]) ).
cnf(c_0_272,plain,
~ product(e_2,e_5,e_3),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_268]),c_0_55])]) ).
cnf(c_0_273,negated_conjecture,
( ~ product(e_2,e_5,e_4)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_54,c_0_269]) ).
cnf(c_0_274,negated_conjecture,
( ~ product(e_2,e_4,X1)
| product(X1,e_1,e_2)
| product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_124,c_0_260]) ).
cnf(c_0_275,negated_conjecture,
( ~ product(e_3,e_4,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_194,c_0_175]) ).
cnf(c_0_276,plain,
( product(e_3,e_4,e_5)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_71]),c_0_270]) ).
cnf(c_0_277,plain,
( product(e_2,e_5,e_1)
| product(e_2,e_5,e_2)
| product(e_2,e_5,e_4) ),
inference(sr,[status(thm)],[c_0_271,c_0_272]) ).
cnf(c_0_278,negated_conjecture,
~ product(e_2,e_5,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_213,c_0_273]),c_0_55])]) ).
cnf(c_0_279,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_274,c_0_265]) ).
cnf(c_0_280,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_4,e_2)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_5) ),
inference(spm,[status(thm)],[c_0_275,c_0_276]) ).
cnf(c_0_281,plain,
( product(e_2,e_5,e_2)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[c_0_277,c_0_278]) ).
cnf(c_0_282,negated_conjecture,
~ product(e_3,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_279]),c_0_153]) ).
cnf(c_0_283,negated_conjecture,
( ~ product(e_2,e_4,e_5)
| product(e_3,e_4,e_3)
| product(e_3,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_153,c_0_280]) ).
cnf(c_0_284,negated_conjecture,
( ~ product(e_3,e_4,e_3)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_72,c_0_216]) ).
cnf(c_0_285,plain,
( ~ product(e_2,e_3,e_1)
| product(e_2,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_166,c_0_281]) ).
cnf(c_0_286,plain,
( ~ group_element(X1)
| product(X1,e_2,e_1)
| product(X1,e_2,e_2)
| product(X1,e_2,e_3)
| product(X1,e_2,e_4)
| product(X1,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_52,c_0_51]) ).
cnf(c_0_287,plain,
~ product(e_3,e_2,e_3),
inference(spm,[status(thm)],[c_0_250,c_0_55]) ).
cnf(c_0_288,plain,
( product(e_3,e_1,e_4)
| product(e_3,e_1,e_3) ),
inference(sr,[status(thm)],[c_0_146,c_0_282]) ).
cnf(c_0_289,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_4,e_2)
| product(e_2,e_4,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_283,c_0_237]),c_0_284]) ).
cnf(c_0_290,negated_conjecture,
~ product(e_2,e_4,e_2),
inference(spm,[status(thm)],[c_0_188,c_0_265]) ).
cnf(c_0_291,plain,
~ product(e_2,e_3,e_1),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_247,c_0_285]),c_0_55])]) ).
cnf(c_0_292,negated_conjecture,
( ~ product(e_3,e_2,e_1)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_247,c_0_175]) ).
cnf(c_0_293,plain,
( product(e_3,e_2,e_5)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_286,c_0_71]),c_0_287]) ).
cnf(c_0_294,plain,
( ~ product(e_3,e_2,e_4)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_213,c_0_288]) ).
cnf(c_0_295,negated_conjecture,
( product(e_3,e_4,e_2)
| product(e_2,e_5,e_1) ),
inference(sr,[status(thm)],[c_0_289,c_0_290]) ).
cnf(c_0_296,plain,
( product(e_2,e_3,e_4)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[c_0_251,c_0_291]) ).
cnf(c_0_297,negated_conjecture,
( product(e_2,e_5,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_4)
| product(e_3,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_292,c_0_293]) ).
cnf(c_0_298,plain,
~ product(e_3,e_2,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_294]),c_0_55])]) ).
cnf(c_0_299,negated_conjecture,
( ~ product(e_3,e_2,e_2)
| product(e_2,e_5,e_1) ),
inference(spm,[status(thm)],[c_0_241,c_0_295]) ).
cnf(c_0_300,plain,
~ product(e_3,e_5,e_5),
inference(spm,[status(thm)],[c_0_138,c_0_55]) ).
cnf(c_0_301,plain,
( ~ product(e_3,e_5,e_4)
| product(e_3,e_1,e_3) ),
inference(spm,[status(thm)],[c_0_129,c_0_288]) ).
cnf(c_0_302,negated_conjecture,
( ~ product(e_3,e_2,X1)
| product(X1,e_4,e_3)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_124,c_0_296]) ).
cnf(c_0_303,negated_conjecture,
( product(e_3,e_2,e_5)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_297,c_0_298]),c_0_299]) ).
cnf(c_0_304,plain,
( product(e_3,e_5,e_4)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_234,c_0_71]),c_0_300]) ).
cnf(c_0_305,plain,
~ product(e_3,e_5,e_4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_198,c_0_301]),c_0_55])]) ).
cnf(c_0_306,plain,
( ~ product(X1,X2,e_2)
| ~ product(X1,X2,e_1) ),
inference(spm,[status(thm)],[c_0_43,c_0_117]) ).
cnf(c_0_307,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_2,e_5,e_1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_302,c_0_303]),c_0_221]) ).
cnf(c_0_308,plain,
( product(e_3,e_5,e_1)
| product(e_3,e_5,e_2)
| product(e_3,e_5,e_3) ),
inference(sr,[status(thm)],[c_0_304,c_0_305]) ).
cnf(c_0_309,negated_conjecture,
~ product(e_2,e_5,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_306,c_0_307]),c_0_166]) ).
cnf(c_0_310,plain,
( ~ product(e_2,e_5,e_1)
| product(e_3,e_5,e_3)
| product(e_3,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_153,c_0_308]) ).
cnf(c_0_311,plain,
product(e_2,e_5,e_1),
inference(sr,[status(thm)],[c_0_281,c_0_309]) ).
cnf(c_0_312,plain,
( product(e_3,e_5,e_2)
| product(e_3,e_5,e_3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_310,c_0_311])]) ).
cnf(c_0_313,plain,
product(e_3,e_5,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_166,c_0_312]),c_0_55])]) ).
cnf(c_0_314,plain,
( product(e_3,e_2,e_1)
| product(e_3,e_2,e_2)
| product(e_3,e_2,e_5) ),
inference(sr,[status(thm)],[c_0_293,c_0_298]) ).
cnf(c_0_315,plain,
~ product(e_3,e_2,e_2),
inference(spm,[status(thm)],[c_0_247,c_0_313]) ).
cnf(c_0_316,negated_conjecture,
( ~ product(e_3,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_230]),c_0_161]) ).
cnf(c_0_317,plain,
( product(e_3,e_2,e_5)
| product(e_3,e_2,e_1) ),
inference(sr,[status(thm)],[c_0_314,c_0_315]) ).
cnf(c_0_318,plain,
( product(e_5,e_1,e_3)
| product(e_5,e_1,e_2) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[c_0_152,c_0_282]),c_0_316]) ).
cnf(c_0_319,negated_conjecture,
( ~ product(e_2,e_3,X1)
| product(X1,e_1,e_2)
| product(e_3,e_2,e_5) ),
inference(spm,[status(thm)],[c_0_124,c_0_317]) ).
cnf(c_0_320,plain,
( ~ product(e_5,e_4,e_3)
| product(e_5,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_104,c_0_318]) ).
cnf(c_0_321,negated_conjecture,
( product(e_3,e_2,e_5)
| product(e_2,e_3,e_2) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_319,c_0_296]),c_0_164]) ).
cnf(c_0_322,negated_conjecture,
( product(e_2,e_1,e_2)
| product(e_3,e_2,e_5)
| product(e_3,e_2,e_2) ),
inference(spm,[status(thm)],[c_0_262,c_0_314]) ).
cnf(c_0_323,plain,
( ~ product(e_5,e_4,e_3)
| ~ product(e_2,e_1,e_2) ),
inference(spm,[status(thm)],[c_0_151,c_0_320]) ).
cnf(c_0_324,negated_conjecture,
( product(e_2,e_3,e_2)
| product(e_5,e_4,e_3) ),
inference(spm,[status(thm)],[c_0_302,c_0_321]) ).
cnf(c_0_325,negated_conjecture,
( product(e_3,e_2,e_5)
| product(e_2,e_1,e_2) ),
inference(sr,[status(thm)],[c_0_322,c_0_315]) ).
cnf(c_0_326,negated_conjecture,
~ product(e_2,e_1,e_2),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_323,c_0_324]),c_0_198]) ).
cnf(c_0_327,negated_conjecture,
product(e_3,e_2,e_5),
inference(sr,[status(thm)],[c_0_325,c_0_326]) ).
cnf(c_0_328,negated_conjecture,
( ~ product(e_2,e_3,X1)
| product(X1,e_5,e_2) ),
inference(spm,[status(thm)],[c_0_124,c_0_327]) ).
cnf(c_0_329,negated_conjecture,
( product(e_4,e_5,e_2)
| product(e_2,e_3,e_2) ),
inference(spm,[status(thm)],[c_0_328,c_0_296]) ).
cnf(c_0_330,negated_conjecture,
product(e_2,e_3,e_2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_161,c_0_329]),c_0_313])]) ).
cnf(c_0_331,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_250,c_0_330]),c_0_55])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GRP125-3.005 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.46 % Computer : n013.cluster.edu
% 0.18/0.46 % Model : x86_64 x86_64
% 0.18/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.46 % Memory : 8046.5625MB
% 0.18/0.46 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sun Sep 20 19:59:21 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.54 Running first-order theorem proving
% 0.23/0.54 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.26/1.69 % Version: 3.5.1
% 7.26/1.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.26/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.26/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.26/1.69 % Starting new_bool_3 with 300s (1) cores
% 7.26/1.69 % Starting new_bool_1 with 300s (1) cores
% 7.26/1.69 % Starting sh5l with 300s (1) cores
% 7.26/1.69 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3284036 completed with status 0
% 7.26/1.69 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 7.26/1.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.26/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.26/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.26/1.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.26/1.69 % No SInE strategy applied
% 7.26/1.69 % Search class: FGHNF-FFMM00-SFFFFFNN
% 7.26/1.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.26/1.69 % Starting SubtermCWHack with 136s (1) cores
% 7.26/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.26/1.69 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 7.26/1.69 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 7.26/1.69 % Starting G-E--_208_B07--C_F1_SE_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 7.26/1.69 % G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with pid 3284043 completed with status 0
% 7.26/1.69 % Result found by G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI
% 7.26/1.69 % Preprocessing class: FSMSSMSSSSSNFFN.
% 7.26/1.69 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 7.26/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 7.26/1.69 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 7.26/1.69 % No SInE strategy applied
% 7.26/1.69 % Search class: FGHNF-FFMM00-SFFFFFNN
% 7.26/1.69 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 7.26/1.69 % Starting SubtermCWHack with 136s (1) cores
% 7.26/1.69 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 7.26/1.69 % Starting H----_011_C07_F1_PI_AE_OS_R8_SP_S1U with 136s (1) cores
% 7.26/1.69 % Starting G----_425_C05_02_F1_SE_CS_SP_PS_RG_S04AI with 136s (1) cores
% 7.26/1.69 % Preprocessing time : 0.002 s
% 7.26/1.69 % Presaturation interreduction done
% 7.26/1.69
% 7.26/1.69 % Proof found!
% 7.26/1.69 % SZS status Unsatisfiable
% 7.26/1.69 % SZS output start CNFRefutation
% See solution above
% 7.26/1.69 % Parsed axioms : 58
% 7.26/1.69 % Removed by relevancy pruning/SinE : 0
% 7.26/1.69 % Initial clauses : 58
% 7.26/1.69 % Removed in clause preprocessing : 0
% 7.26/1.69 % Initial clauses in saturation : 58
% 7.26/1.69 % Processed clauses : 2613
% 7.26/1.69 % ...of these trivial : 2
% 7.26/1.69 % ...subsumed : 859
% 7.26/1.69 % ...remaining for further processing : 1752
% 7.26/1.69 % Other redundant clauses eliminated : 0
% 7.26/1.69 % Clauses deleted for lack of memory : 0
% 7.26/1.69 % Backward-subsumed : 999
% 7.26/1.69 % Backward-rewritten : 156
% 7.26/1.69 % Generated clauses : 6126
% 7.26/1.69 % ...of the previous two non-redundant : 5600
% 7.26/1.69 % ...aggressively subsumed : 0
% 7.26/1.69 % Contextual simplify-reflections : 199
% 7.26/1.69 % Paramodulations : 6039
% 7.26/1.69 % Factorizations : 0
% 7.26/1.69 % NegExts : 0
% 7.26/1.69 % Equation resolutions : 0
% 7.26/1.69 % Disequality decompositions : 0
% 7.26/1.69 % Total rewrite steps : 850
% 7.26/1.69 % ...of those cached : 818
% 7.26/1.69 % Propositional unsat checks : 0
% 7.26/1.69 % Propositional check models : 0
% 7.26/1.69 % Propositional check unsatisfiable : 0
% 7.26/1.69 % Propositional clauses : 0
% 7.26/1.69 % Propositional clauses after purity: 0
% 7.26/1.69 % Propositional unsat core size : 0
% 7.26/1.69 % Propositional preprocessing time : 0.000
% 7.26/1.69 % Propositional encoding time : 0.000
% 7.26/1.69 % Propositional solver time : 0.000
% 7.26/1.69 % Success case prop preproc time : 0.000
% 7.26/1.69 % Success case prop encoding time : 0.000
% 7.26/1.69 % Success case prop solver time : 0.000
% 7.26/1.69 % Current number of processed clauses : 452
% 7.26/1.69 % Positive orientable unit clauses : 37
% 7.26/1.69 % Positive unorientable unit clauses: 0
% 7.26/1.69 % Negative unit clauses : 87
% 7.26/1.69 % Non-unit-clauses : 328
% 7.26/1.69 % Current number of unprocessed clauses: 2556
% 7.26/1.69 % ...number of literals in the above : 17247
% 7.26/1.69 % Current number of archived formulas : 0
% 7.26/1.69 % Current number of archived clauses : 1300
% 7.26/1.69 % Clause-clause subsumption calls (NU) : 351911
% 7.26/1.69 % Rec. Clause-clause subsumption calls : 114477
% 7.26/1.69 % Non-unit clause-clause subsumptions : 1353
% 7.26/1.69 % Unit Clause-clause subsumption calls : 17851
% 7.26/1.69 % Rewrite failures with RHS unbound : 0
% 7.26/1.69 % BW rewrite match attempts : 59
% 7.26/1.69 % BW rewrite match successes : 10
% 7.26/1.69 % Condensation attempts : 0
% 7.26/1.69 % Condensation successes : 0
% 7.26/1.69 % Termbank termtop insertions : 92546
% 7.26/1.69 % Search garbage collected termcells : 114
% 7.26/1.69
% 7.26/1.69 % -------------------------------------------------
% 7.26/1.69 % User time : 0.699 s
% 7.26/1.69 % System time : 0.014 s
% 7.26/1.69 % Total time : 0.713 s
% 7.26/1.69 % Maximum resident set size: 3664 pages
% 7.26/1.69
% 7.26/1.69 % -------------------------------------------------
% 7.26/1.69 % User time : 4.745 s
% 7.26/1.69 % System time : 0.090 s
% 7.26/1.69 % Total time : 4.835 s
% 7.26/1.69 % Maximum resident set size: 4864 pages
% 7.26/1.69 % E exiting
%------------------------------------------------------------------------------